The thermodynamic response of materials during plastic deformation originates from the imposed plastic strain rate. Thus the precise thermodynamic parameter has to be measured during changes in the plastic strain rate. The method described herein permits this desired controlled plastic strain rate change. Even the most sophisticated materials testing system currently available permits only total strain rate changes, that is the changes in the sum of the plastic and elastic strain rate of the specimen to be determined. The following analysis illustrates that the thermodynamic parameter, the activation volume, v is determined by performing plastic strain rate change tests. Furthermore, it will show how the elastic strain of the specimen and the frame of the testing apparatus which interferes with the plastic strain rate change is removed by the proposed method.
All solids which are deformed in a non-elastic manner under an applied stress .sigma. are aided in the microplastic deformation process by the thermal energy. The most simple analytical form in which this stress-aided process can be described is by the rate equation ##EQU1## where .epsilon. is the enforced plastic strain rate; .epsilon..sub.o, the number of strain centres which can participate in the deformation process; .nu., the frequency of attempts to overcome the obstacle preventing the incremental strain process from taking place; .DELTA.G, the total free energy required to overcome the obstacle at 0.degree. K.; v, the activation volume; k, the Boltzmann constant, and T, the test temperature in Kelvin.
Thus ##EQU2## Hence experimental v can be defined as ##EQU3## where S is called the strain rate sensitivity and defined as ##EQU4## This value is identical to the theoretical one if the first two terms of the right side are zero. If these terms are not zero, their temperature and strain rate dependence can reveal the atomic/molecular processes responsible for the deviation. The above definition of v shows that, ideally, the change in stress value .sigma..sub.1 at .epsilon..sub.1 to .sigma..sub.2 can be measured at .epsilon..sub.2 if an instantaneous plastic strain rate change is made. Thus the change .DELTA..sigma. is an elastic response of the microplastic process, that is if .epsilon..sub.2 &lt;.epsilon..sub.1 then the stress can be lowered just enough so that the reduction in ##EQU5## is in the same ratio as that for the plastic strain rate .epsilon..
In practice, however, tensile testing machines and systems and the specimens used therein have an elastic response which generally completely masks the reduction in stress effect. The stress change is given by ##EQU6## x=.epsilon.L+.sigma.L(1/E+1/M). x is the displacement rate (the change in distance between the grips of the specimens) and is the parameter usually controlled by the operator; v, the activation volume; .epsilon., the plastic strain rate; L, the current specimen length; E, the Young's Modulus of the specimen; M, the machine stiffness component including the linkages (the effective spring constant of the loading train).
In order to achieve plastic strain rate changes, x must be made equal to .epsilon. by imposing .sigma.L (1/E+1/M) to become zero.